Finite Group Databasebeta

← #28364182

Subgroups — #28364182

Order 13952.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812690C211yesmaximal, characteristic
2C2×#16812624C211yesmaximal, characteristic
3C2×#16812622C211yesmaximal, characteristic
4#20294931C211yesmaximal, characteristic
5#20294788C211yesmaximal, characteristic
6#20294780C211yesmaximal, characteristic
7#340×C109C211yesmaximal, characteristic
8C22×Dic218C2211yescharacteristic
9C22×#11724784C2211yescharacteristic
10#16812690—22no—
11#16812690—22no—
12C2×C4⋊Dic109—21no—
13C2×C4⋊Dic109C2211yescharacteristic
14C2×#13182008—21no—
15C2×C4×Dic109C2211yescharacteristic
16#16812624—22no—
17#16812622—22no—
18#16812606—21no—
19#16812606—21no—
20C22×C8×C109C2211yescharacteristic
21C2×C4⋊C4×C109C2211yescharacteristic
22C2×C4⋊C4×C109C2211yescharacteristic
23C2×Dic218—21no—
24C2×Dic218—21no—
25C2×Dic218—21no—
26C2×Dic218—21no—
27C2×Dic218—21no—
28C2×Dic218Q812yes—
29C22×Dic109—21no—
30C22×Dic109—21no—
31C22×Dic109D411yescharacteristic
32C22×Dic109D411yescharacteristic
33C2×#11724784—21no—
34C2×#11724784—21no—
35C2×#11724784—21no—
36C4⋊Dic109—24no—
37C4⋊Dic109—21no—
38C4⋊Dic109D412yes—
39#13182008—24no—
40C4×Dic109—21no—
41C4×Dic109—21no—
42C22×C4×C109—21no—
43C22×C4×C109—21no—
44C22×C4×C109C2311yescharacteristic
45C2×C8×C109—21no—
46C2×C8×C109—21no—
47C2×C8×C109—21no—
48C4⋊C4×C109—21no—
49C4⋊C4×C109—21no—
50C4⋊C4×C109—21no—
51C4⋊C4×C109D412yes—
52C23×C109C2×D411yescharacteristic
53C2×C4×C109—22no—
54C2×C4×C109—41no—
55C2×C4×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109—41no—
58C2×C4×C109—41no—
59C2×C4×C109C2×D411yescharacteristic
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109C2×Q811yescharacteristic
62C2×C4×C109#4111yescharacteristic
63C2×C4×C109#4111yescharacteristic
64C2×C4×C109#4111yescharacteristic
65C2×Dic109—21no—
66C2×Dic109—21no—
67C2×Dic109—22no—
68C2×Dic109—22no—
69C2×Dic109—21no—
70C2×Dic109—21no—
71C2×Dic109—21no—
72C2×Dic109—21no—
73C2×Dic109—41no—
74C2×Dic109—41no—
75C2×Dic109—41no—
76C2×Dic109—41no—
77Dic218—22no—
78Dic218—22no—
79Dic218—41no—
80Dic218—41no—
81C8×C109—41no—
82#11724784—41no—
83C22×C109#12011yescharacteristic
84C22×C109C22⋊Q811yescharacteristic
85C22×C109#12411yescharacteristic
86C22×C109#13511yescharacteristic
87C22×C109#13511yescharacteristic
88C22×C109#13711yescharacteristic
89C22×C109#13711yescharacteristic
90C4×C109—42no—
91C4×C109—81no—
92C4×C109C22⋊Q811yescharacteristic
93C4×C109C22⋊Q811yescharacteristic
94C4×C109#12411yescharacteristic
95C4×C109#12411yescharacteristic
96Dic109—42no—
97Dic109—41no—
98Dic109—41no—
99Dic109—42no—
100C2×C109#39311yescharacteristic
101C2×C109#45211yescharacteristic
102C2×C109#45211yescharacteristic
103C2×C109#47911yescharacteristic
104C2×C109#47911yescharacteristic
105C2×C109#48811yescharacteristic
106C2×C109#49111yescharacteristic
107#2026—1091nomaximal, Sylow
108C109#202611yescharacteristic, complemented, Sylow
109C2×#125—1091no—
110C2×#103—1091no—
111C2×#103—1091no—
112#391—1091no—
113#340—1091no—
114#340D10911yescharacteristic
115#336—1091no—
116C22×Q8—1091no—
117C22×C8—1091no—
118C22×C8C2×D10911yescharacteristic
119#125—2182no—
120#125—2182no—
121C2×C4⋊C4—1091no—
122C2×C4⋊C4—2181no—
123C2×C4⋊C4—2181no—
124C2×C4⋊C4C2×D10911yescharacteristic
125C2×C4⋊C4C2×D10911yescharacteristic
126C2×C42—1091no—
127#103—2182no—
128#103—2182no—
129#95—2181no—
130#95—2181no—
131C2×Q8—1092no—
132C2×Q8—2181no—
133C2×Q8—2181no—
134C2×Q8—2181no—
135C2×Q8—2181no—
136C2×Q8—2181no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—1091no—
140C22×C4—1091no—
141C22×C4—2181no—
142C22×C4—2181no—
143C22×C4C22×D10911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2181no—
148C2×C8—2181no—
149C2×C8—2181no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—1092no—
154C4⋊C4—2184no—
155C4⋊C4—2184no—
156C4⋊C4—2181no—
157C4⋊C4D43612yes—
158C42—2181no—
159C42—2181no—
160C23D4×D10911yescharacteristic
161Q8—4361no—
162Q8—4361no—
163Q8—2182no—
164Q8—2182no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4361no—
172C2×C4—4361no—
173C2×C4—4361no—
174C2×C4—4361no—
175C2×C4—2181no—
176C2×C4—2181no—
177C2×C4—2182no—
178C2×C4—2182no—
179C2×C4—2181no—
180C2×C4—2181no—
181C2×C4—2181no—
182C2×C4—2181no—
183C2×C4D4×D10911yescharacteristic
184C2×C4C2×D43611yescharacteristic
185C2×C4Q8×D10911yescharacteristic
186C2×C4#1318202811yescharacteristic
187C2×C4#1318202911yescharacteristic
188C2×C4#1318202911yescharacteristic
189C8—41no—
190C8—4361no—
191C22#1681266911yescharacteristic
192C22#1681267711yescharacteristic
193C22#1681268511yescharacteristic
194C22#1681271811yescharacteristic
195C22#1681272011yescharacteristic
196C22#1681272811yescharacteristic
197C22#1681273111yescharacteristic
198C4—42no—
199C4—81no—
200C4—4361no—
201C4—4362no—
202C4—4361no—
203C4—4362no—
204C4#1681267711yescharacteristic
205C4#1681267911yescharacteristic
206C4#1681268511yescharacteristic
207C4#1681268711yescharacteristic
208C2#2029493911yescharacteristic
209C2#2029518911yescharacteristic
210C2#2029519111yescharacteristic
211C2#2029533211yescharacteristic
212C2#2029533611yescharacteristic
213C2#2029537911yescharacteristic
214C2#2029539311yescharacteristic
subgroupG/H
centerC23D4×D109
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#340×C109C2
socle, prime radicalC23×C109C2×D4
hypercenter#340D109
hypocenterC109#2026
LCSG ▷ C22×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
108. C109#2026semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168126902
C2×#168126242
C2×#168126222
#202949312
#202947882
#202947802
#340×C1092
#2026109